November 27, 2020
Space Shuttle Challenger exploded moments after launching on January 28, 1986. Source: CNN news
Source: https://www.kaggle.com/agirlcoding/all-space-missions-from-1957
Categorical Data Analysis with Logistic Regression \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1} + \beta_2 X_{2} + \ldots + \beta_k X_{k}\]
Single Logistic Regression models \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1}\]
Response variable: Mission Outcome (Success: Yes/No)
Predictors: Rocket Status (Active/Retired), Country (USA/Russia), Space Race Decade (1960s/1970s)
\(H_o:\) \(\beta_1 = 0\)
\(H_a:\) \(\beta_1 \ne 0\)
Test statistic: \(\displaystyle z = \frac{\hat{\beta_1}}{s(\hat{\beta_1})}\)
p-value = 2*pnorm(z, lower.tail = FALSE)
\[\hat{\beta_1} \pm z_{({1 - \alpha/2})} s(\hat{\beta_1})\]
Estimate Std. Error z value Pr(>|z|) (Intercept) 2.0842255 0.05362567 38.866192 0.000000000 ActiveYes 0.5280206 0.15084041 3.500525 0.000464343
ActiveYes 2.5 % 97.5 % 1.695573 1.272852 2.301764
Estimate Std. Error z value Pr(>|z|) (Intercept) 2.01575 0.08469 23.80166 0.00000 CountryRussia 0.31928 0.11446 2.78945 0.00528
CountryRussia 2.5 % 97.5 %
1.3761360 0.5791487 1.0988476 1.7216396